THE UNIVERSITY OF BRITISH COLUMBIA
Wed. 22 Mar. 2006 - finish by Wed. 29 Mar.
- (p. 449, Problem 11.2) - Electric Dipolar Radiation:
can be expressed in "coordinate-free" form by writing
. Do so, and
similarly for Equations
- Atomic Dipoles:
Explain why you can safely assume
for an atom with magnetic dipole moment
and electric dipole moment , assuming
typical values of relevant physical quantities.
- (p. 473-474, Problem 11.22) - Broadcasting KRUD:
A radio tower rises to a height h above flat horizontal ground.
At the top is a magnetic dipole antenna of radius b,
with its axis vertical. FM station KRUD broadcasts from this antenna
at angular frequency , with a total radiated power P
(averaged, of course, over a full cycle). Neighbors have complained
about problems they attribute to excessive radiation from the tower -
interference with their stereo systems, mechanical garage doors
opening and closing mysteriously, and a variety of suspicious
medical problems. But the city engineer who measured the radiation
at the base of the tower found it to be well below the accepted standard.
You have been hired by the Neighborhood Association
to assess the engineer's report.
- In terms of the variables given
(not all of which may be relevant, of course)
find the formula for the intensity of the radiation at ground level,
a distance R away from the base of the tower.
You may assume that
[Note: we are interested only in the magnitude
of the radiation, not in its direction -
when measurements are taken, the detector will be aimed
directly at the antenna.]
- How far from the base of the tower should the engineer
have made the measurement? What is the formula for the intensity
at this location?
- KRUD's actual power output is 35 kilowatts,
its frequency is 90 MHz, the antenna's radius is 6 cm,
and the height of the tower is 200 m.
The city's radio-emission limit is 200 microwatts/cm2.
Is KRUD in compliance?
- (p. 474, Problem 11.23) - Earth as a Pulsar:
The magnetic north pole of the Earth does not coincide
with the geographic North Pole - in fact, it's off by about
7 at present.1Relative to the fixed axis of rotation, therefore,
the magnetic dipole moment vector of the Earth is changing with time,
so the Earth must be giving off magnetic dipole radiation.
- Find the formula for the total power radiated,
in terms of the following parameters:
(the angle between the geographic and magnetic north poles),
M (the magnitude of the Earth's magnetic dipole moment),
and (the angular velocity of rotation of the Earth).
[Hint: refer to Prob. 11.4 or Prob. 11.12.]
- Using the fact that the Earth's magnetic field is
about half a gauss at the Equator, estimate
the magnetic dipole moment M of the Earth.
- Find the power radiated.
[Your answer should be several times 10-5 W.]
- Pulsars are thought to be rotating neutron stars,
with a typical radius of about km,
a typical surface magnetic field of T
and a variety of rotational periods T; let's use s.
What sort of radiated power would you expect from such a star?
[See J.P. Ostriker and J.E. Gunn, Astrophys. J. 157,
1395 (1969). Answer:
2 x 1036 W.]
Jess H. Brewer